1 // Ceres Solver - A fast non-linear least squares minimizer
2 // Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
3 // http://code.google.com/p/ceres-solver/
4 //
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6 // modification, are permitted provided that the following conditions are met:
7 //
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9 // this list of conditions and the following disclaimer.
10 // * Redistributions in binary form must reproduce the above copyright notice,
11 // this list of conditions and the following disclaimer in the documentation
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14 // used to endorse or promote products derived from this software without
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16 //
17 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
18 // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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28 //
29 // Author: sameeragarwal@google.com (Sameer Agarwal)
30
31 #include "ceres/iterative_schur_complement_solver.h"
32
33 #include <algorithm>
34 #include <cstring>
35 #include <vector>
36
37 #include "Eigen/Dense"
38 #include "ceres/block_sparse_matrix.h"
39 #include "ceres/block_structure.h"
40 #include "ceres/conjugate_gradients_solver.h"
41 #include "ceres/implicit_schur_complement.h"
42 #include "ceres/internal/eigen.h"
43 #include "ceres/internal/scoped_ptr.h"
44 #include "ceres/linear_solver.h"
45 #include "ceres/preconditioner.h"
46 #include "ceres/schur_jacobi_preconditioner.h"
47 #include "ceres/triplet_sparse_matrix.h"
48 #include "ceres/types.h"
49 #include "ceres/visibility_based_preconditioner.h"
50 #include "ceres/wall_time.h"
51 #include "glog/logging.h"
52
53 namespace ceres {
54 namespace internal {
55
IterativeSchurComplementSolver(const LinearSolver::Options & options)56 IterativeSchurComplementSolver::IterativeSchurComplementSolver(
57 const LinearSolver::Options& options)
58 : options_(options) {
59 }
60
~IterativeSchurComplementSolver()61 IterativeSchurComplementSolver::~IterativeSchurComplementSolver() {
62 }
63
SolveImpl(BlockSparseMatrix * A,const double * b,const LinearSolver::PerSolveOptions & per_solve_options,double * x)64 LinearSolver::Summary IterativeSchurComplementSolver::SolveImpl(
65 BlockSparseMatrix* A,
66 const double* b,
67 const LinearSolver::PerSolveOptions& per_solve_options,
68 double* x) {
69 EventLogger event_logger("IterativeSchurComplementSolver::Solve");
70
71 CHECK_NOTNULL(A->block_structure());
72
73 // Initialize a ImplicitSchurComplement object.
74 if (schur_complement_ == NULL) {
75 schur_complement_.reset(
76 new ImplicitSchurComplement(options_.elimination_groups[0],
77 options_.preconditioner_type == JACOBI));
78 }
79 schur_complement_->Init(*A, per_solve_options.D, b);
80
81 const int num_schur_complement_blocks =
82 A->block_structure()->cols.size() - options_.elimination_groups[0];
83 if (num_schur_complement_blocks == 0) {
84 VLOG(2) << "No parameter blocks left in the schur complement.";
85 LinearSolver::Summary cg_summary;
86 cg_summary.num_iterations = 0;
87 cg_summary.termination_type = TOLERANCE;
88 schur_complement_->BackSubstitute(NULL, x);
89 return cg_summary;
90 }
91
92 // Initialize the solution to the Schur complement system to zero.
93 //
94 // TODO(sameeragarwal): There maybe a better initialization than an
95 // all zeros solution. Explore other cheap starting points.
96 reduced_linear_system_solution_.resize(schur_complement_->num_rows());
97 reduced_linear_system_solution_.setZero();
98
99 // Instantiate a conjugate gradient solver that runs on the Schur complement
100 // matrix with the block diagonal of the matrix F'F as the preconditioner.
101 LinearSolver::Options cg_options;
102 cg_options.max_num_iterations = options_.max_num_iterations;
103 ConjugateGradientsSolver cg_solver(cg_options);
104 LinearSolver::PerSolveOptions cg_per_solve_options;
105
106 cg_per_solve_options.r_tolerance = per_solve_options.r_tolerance;
107 cg_per_solve_options.q_tolerance = per_solve_options.q_tolerance;
108
109 Preconditioner::Options preconditioner_options;
110 preconditioner_options.type = options_.preconditioner_type;
111 preconditioner_options.sparse_linear_algebra_library_type =
112 options_.sparse_linear_algebra_library_type;
113 preconditioner_options.num_threads = options_.num_threads;
114 preconditioner_options.row_block_size = options_.row_block_size;
115 preconditioner_options.e_block_size = options_.e_block_size;
116 preconditioner_options.f_block_size = options_.f_block_size;
117 preconditioner_options.elimination_groups = options_.elimination_groups;
118
119 switch (options_.preconditioner_type) {
120 case IDENTITY:
121 break;
122 case JACOBI:
123 preconditioner_.reset(
124 new SparseMatrixPreconditionerWrapper(
125 schur_complement_->block_diagonal_FtF_inverse()));
126 break;
127 case SCHUR_JACOBI:
128 if (preconditioner_.get() == NULL) {
129 preconditioner_.reset(
130 new SchurJacobiPreconditioner(*A->block_structure(),
131 preconditioner_options));
132 }
133 break;
134 case CLUSTER_JACOBI:
135 case CLUSTER_TRIDIAGONAL:
136 if (preconditioner_.get() == NULL) {
137 preconditioner_.reset(
138 new VisibilityBasedPreconditioner(*A->block_structure(),
139 preconditioner_options));
140 }
141 break;
142 default:
143 LOG(FATAL) << "Unknown Preconditioner Type";
144 }
145
146 bool preconditioner_update_was_successful = true;
147 if (preconditioner_.get() != NULL) {
148 preconditioner_update_was_successful =
149 preconditioner_->Update(*A, per_solve_options.D);
150 cg_per_solve_options.preconditioner = preconditioner_.get();
151 }
152
153 event_logger.AddEvent("Setup");
154
155 LinearSolver::Summary cg_summary;
156 cg_summary.num_iterations = 0;
157 cg_summary.termination_type = FAILURE;
158
159 if (preconditioner_update_was_successful) {
160 cg_summary = cg_solver.Solve(schur_complement_.get(),
161 schur_complement_->rhs().data(),
162 cg_per_solve_options,
163 reduced_linear_system_solution_.data());
164 if (cg_summary.termination_type != FAILURE) {
165 schur_complement_->BackSubstitute(
166 reduced_linear_system_solution_.data(), x);
167 }
168 }
169
170 VLOG(2) << "CG Iterations : " << cg_summary.num_iterations;
171
172 event_logger.AddEvent("Solve");
173 return cg_summary;
174 }
175
176 } // namespace internal
177 } // namespace ceres
178